Find the magnitude of the magnetic force on a proton moving at 2.5 ×10^5 m / s (a) perpendicular

step 1 So in this example, we are given a proton moving in a magnetic field, and we are asked to find t

Find the magnitude of the magnetic force on a proton moving...

Find the magnitude of the magnetic force on a proton moving at $2.5 \times 10^{5} \mathrm{m} / \mathrm{s}$ (a) perpendicular; (b) at $30^{\circ} ;$ (c) parallel to a $0.50-\mathrm{T}$ magnetic field.

Key Concepts

Lorentz Force

The Lorentz force is the fundamental concept describing how charged particles experience a force when moving through electric and magnetic fields. In the context of a magnetic field, this force acts perpendicular to both the velocity of the particle and the magnetic field, and its magnitude is given by the product of the charge, the speed of the particle, the magnetic field strength, and the sine of the angle between the velocity and the magnetic field.

Magnetic Force Equation

The magnetic force acting on a moving charge is quantifiably described by the equation F = qvB sin?, where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and ? is the angle between the velocity vector and the magnetic field vector. This equation highlights the linear dependence on charge, speed, magnetic field strength, and the sine of the angle.

Angle Dependence in Magnetic Interaction

The sine term in the magnetic force equation represents the dependency of the force magnitude on the angle between the charged particle's velocity and the magnetic field. When the particle moves perpendicular to the field (? = 90°), sin? is maximized, and the force is at its greatest. Conversely, when the particle moves parallel to the field (? = 0° or 180°), sin? equals zero, and no magnetic force is exerted.

Properties of Charged Particles in Magnetic Fields

Understanding how charged particles such as protons interact with magnetic fields is essential in electromagnetism. Their trajectories under the influence of magnetic forces are governed by the directions and magnitudes specified by the velocity of the particle and the field, leading to phenomena like circular or helical motion depending on the orientation of their velocity relative to the magnetic field.

Transcript

Please give Ace some feedback